What is (\partial)/(\partial x)(2x^2y-y^3+x) ?

The answer to (\partial)/(\partial x)(2x^2y-y^3+x) is 4xy+1

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(\partial)/(\partial x)(2x^2y-y^3+x)

\frac{\partial}{\partial x} (2 x^{2} y - y^{3} + x)

4 x y + 1

Solution steps

\frac{\partial}{\partial x} (2 x^{2} y - y^{3} + x)

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (2 x^{2} y) - \frac{\partial}{\partial x} (y^{3}) + \frac{\partial}{\partial x} (x)

\frac{\partial}{\partial x} (2 x^{2} y) = 4 y x

\frac{\partial}{\partial x} (y^{3}) = 0

\frac{\partial}{\partial x} (x) = 1

= 4 y x - 0 + 1

Simplify

= 4 x y + 1

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What is (\partial)/(\partial x)(2x^2y-y^3+x) ?
The answer to (\partial)/(\partial x)(2x^2y-y^3+x) is 4xy+1